Python

stdlib

• standard library
• great data types and operator overloading
• great program constructs: much more of a "coding" or "programming" language relative to R

#  e.g., loops, dictionaries
# e.g., strings are super easy to use like "arrays" or lists

x=[]
y=""
z=dict()
n=10
for i in range(n):
    x += [i]
    y += str(i)
    z[i]=i
print(len(x), x, type(x))
print(len(y), y, type(y))
print(len(z), z, type(z))

10 [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] <class 'list'>
10 0123456789 <class 'str'>
10 {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9} <class 'dict'>

# e.g., functions, recurssion, conditionals

def fibonacci(sequence=[0,1], steps=6):
    if steps==0:
        return sequence
    else:
        return fibonacci(sequence+[sum(sequence[-2:])], steps=steps-1)
    
print(fibonacci())

[0, 1, 1, 2, 3, 5, 8, 13]

numpy

• 3-4x slower than C++
• ndarrays, broadcasting

import numpy as np

n=1000000

%%timeit
_ = np.arange(n)*np.arange(n)

3.48 ms ± 243 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

%%timeit
_ = [i*j for i,j in zip(range(n),range(n))]

82.9 ms ± 2.4 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)

print(np.zeros(10).reshape(5,2,1))

[[[0.]
  [0.]]

 [[0.]
  [0.]]

 [[0.]
  [0.]]

 [[0.]
  [0.]]

 [[0.]
  [0.]]]

print(np.ones([1,10]))
print(np.ones([10,1]))

np.ones([1,10])*np.ones([10,1])

[[1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]]
[[1.]
 [1.]
 [1.]
 [1.]
 [1.]
 [1.]
 [1.]
 [1.]
 [1.]
 [1.]]

array([[1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]])

scipy

$$\huge \int_{-1}^{1} \frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}} dx$$

import scipy
from scipy import stats

print(scipy.integrate.quad(lambda x: stats.norm.pdf(x), -1, 1))

scipy.special.erf(1/np.sqrt(2)), 2*(stats.norm.cdf(1)-.5)

(0.682689492137086, 7.579375928402476e-15)

(0.6826894921370859, 0.6826894921370859)

scipy.special.erf?

n = 1000
print(stats.norm(loc=1, scale=2).rvs(n))

stats.norm.fit(stats.norm(loc=1, scale=2).rvs(n))

[ 5.02135051e+00  2.40032431e+00  2.30203951e+00  2.30921686e+00
  2.21281026e+00  3.06057433e+00  4.49123612e-01  1.99547849e+00
  3.23260238e-01  4.42212283e+00  3.67051850e+00  8.13393979e-02
 -8.90453860e-01  3.37429503e+00 -5.48993555e+00  6.39233355e+00
  6.07199121e-01  2.68417795e+00 -4.48919290e-01 -1.60186304e+00
  1.39475167e+00  2.84441301e+00 -9.02703935e-02  1.21572897e+00
  1.29009471e+00  9.34116633e-01  3.62024680e+00  3.44931150e+00
  1.24799258e+00 -9.67033980e-02 -2.79635619e+00  5.78220677e-01
  1.27616694e+00  2.00408948e+00  1.50321096e+00 -1.55220524e+00
 -2.95467158e-01  4.08046637e+00  2.54929284e+00  2.99984135e+00
  1.52729362e+00 -2.18543053e+00 -2.50246763e+00  2.81641032e-01
  7.62264514e-01  4.89920110e+00  2.42746520e+00  3.13052446e+00
  2.48973940e+00  2.95222505e+00 -4.24912966e-01  2.09976603e-01
  1.78192472e+00  4.20545238e-01 -3.13420722e-02 -2.11991395e+00
  7.60100342e-02  5.18083537e+00  3.40924443e+00  2.97133590e+00
  1.15346131e+00  3.07879068e+00  2.23228630e+00 -5.67877002e-01
 -2.18844221e+00  2.62021789e-02  9.02075425e-01 -6.16582738e-01
  5.65996626e+00  5.69565768e-01  1.79704834e+00  3.60099299e+00
 -1.22057252e+00  3.28989060e+00  2.28132425e-01  7.70193974e-01
  3.91240952e+00  7.33653024e-01  2.79224326e+00  1.89590051e-01
 -4.60371971e-01  9.13569717e-01  1.24100997e+00  2.50906295e+00
  4.74657658e-01  1.65190910e+00 -1.03561442e+00 -8.12899069e-01
 -3.81810141e+00  1.41968824e+00  9.06889328e-01 -1.28372660e+00
  5.55850566e+00  5.55571349e-01  2.28860901e+00  6.95135430e+00
  4.15166819e-01  3.13410147e+00  3.28941563e-01  1.16100021e+00
  1.31238547e+00  3.85781979e+00 -3.47464361e-01  1.26838040e+00
 -1.22972612e+00  7.65812353e-02 -1.58799732e+00  3.14454027e+00
 -4.06492008e-01  1.70052679e+00  2.91087205e+00  1.72545755e+00
 -4.83878810e-01 -8.46625743e-01 -1.69104871e-01 -1.08982039e-01
 -8.21210407e-01 -3.89051056e+00  2.16333614e+00 -3.11757299e-01
  4.19384471e+00  1.37878564e+00 -3.12167704e-01  7.29043016e-01
  3.06748874e+00 -1.53556556e+00  2.25498263e+00  2.87663435e+00
  2.71909122e+00  6.39419767e+00  1.14972251e+00  2.07491906e+00
  1.48279685e+00  4.39711445e+00  1.15999215e+00  1.70890453e-01
  2.14091039e+00  2.37456956e+00  4.00174748e+00  5.29449498e+00
  4.80602791e-02  4.77941521e-02 -2.72611693e-01 -2.95010935e+00
 -4.93487527e-01  1.32614794e+00 -7.10165409e-02  1.72223172e+00
 -1.60488193e+00  4.29575367e-01  6.73605169e-01  3.01495468e-02
  9.98606337e-01  1.22053582e+00  2.00020793e+00  1.37139431e-01
  2.25635405e+00 -2.92507422e+00  2.19228127e+00 -4.50141257e-01
  1.39214685e+00 -1.67917095e+00  2.15952984e+00  9.65359213e-02
 -1.72706068e+00  3.26078602e+00  3.41152251e+00  3.34278310e+00
  3.22317943e+00  3.76753541e+00  2.30889504e+00  1.33530628e-01
  1.39266095e-01  3.81069251e-01  4.13403647e-02  2.16988023e+00
  1.83113900e-01  2.13488778e+00  6.08875931e+00  2.59295344e+00
  7.41736639e-01  1.00094484e+00  2.73905781e+00  3.28129292e+00
  2.06527314e+00 -1.08751266e+00  1.84837763e+00  5.37728094e-02
 -1.37210384e+00  2.77485429e+00 -1.28645295e+00  2.18076013e+00
  2.17106400e+00  5.69036400e-01 -2.31765364e+00  1.35754461e-01
 -3.24810484e-01  4.11358176e-01  1.53482803e+00 -2.06375845e+00
  1.19407605e+00  1.90868630e+00 -1.60689418e+00  2.18687494e+00
  1.42522428e+00 -3.51541544e+00  4.40903320e+00 -7.14372230e-02
  1.39530044e+00 -1.85882008e+00  3.12905993e+00  1.20198122e+00
  7.05579531e-01  5.36253856e-01  4.34264751e+00 -1.61231964e+00
 -1.52751248e+00  3.73495130e+00  8.69595332e-01  2.85144007e+00
  1.87524123e+00  2.74887322e+00 -1.12620882e+00  1.47694279e+00
 -1.71970378e-01  1.20942975e+00  3.18859326e+00 -3.48933241e-01
  2.49279123e+00  4.05902019e+00  1.32251715e+00  1.41501310e+00
  2.27849788e+00 -5.23894537e-01  1.49414985e+00  9.33630256e-01
  3.69884567e+00 -9.09700951e-01  7.49986729e-01  4.71157658e-02
  1.58133188e+00  1.72173930e-01  7.15988366e-01 -7.64765974e-01
  3.99516015e+00 -7.75689440e-01  4.01141714e-01 -2.39615369e+00
 -1.58469712e+00  2.34068182e+00 -6.33711877e-01  1.39363600e+00
 -7.58483074e-01  1.19477482e+00  3.37246357e+00  2.05929623e+00
 -4.67597669e-01 -1.91722889e-01 -2.80244185e+00 -1.68459157e+00
  1.87790985e+00  3.54390341e+00  2.74654536e+00  3.26699710e+00
 -1.47180662e-01  5.31516377e+00  2.05147739e+00 -1.09045866e+00
  3.22342910e+00 -3.04532178e+00  3.18041213e+00  3.22933961e+00
 -8.55045489e-01 -4.96024127e-01  2.61899114e-01  1.69412922e+00
  1.44982979e+00 -8.17786399e-01  5.34925298e-02 -1.12675163e+00
  4.85939145e-01  1.89230456e+00  1.36085931e+00  2.98511546e-01
  3.35521191e+00  2.95257814e+00 -2.49891159e+00  1.96431713e+00
 -1.52893217e-02  3.38059279e+00 -1.65953738e+00  1.19733622e+00
 -5.51680026e-01  3.72307066e+00  2.56541743e+00 -2.37398401e+00
 -5.42226500e+00 -6.73846292e-01  4.47583603e+00  1.47641162e+00
 -8.51780590e-01  8.49531647e-01  4.23072345e+00 -1.93351573e-03
  3.70825364e+00 -4.39323166e+00  2.54684857e+00  1.34807387e+00
  9.64698149e-02 -8.98978781e-01 -2.17504928e+00  1.25235793e+00
  1.51724770e+00  2.83796269e+00  1.71767552e+00  1.48493543e+00
 -1.97208879e+00  9.37364257e-01  2.19095833e+00  4.88794779e+00
  4.97711844e+00  2.08937515e+00  3.00451387e+00 -7.87137846e-01
  3.94788891e+00  3.32777112e+00  1.72234611e+00  4.97929235e+00
  1.54220565e+00 -2.03790626e+00 -2.04753679e-01  5.72594626e-03
  4.10829057e-01  2.71856096e-01  1.25961017e+00  2.60072157e-01
 -7.83752782e-01 -6.51045665e-01  3.97765285e-01 -6.92927538e-01
  3.69311796e+00 -7.43641633e-02  4.40558049e+00  2.23848184e+00
  1.82106084e-01  3.81521925e+00  4.23385261e+00  4.37703886e-01
  1.22804688e+00  1.07434868e+00  1.98063898e+00  2.04505560e+00
  1.85116543e+00  6.01199804e-01  8.25909961e-01 -1.48816582e-01
  1.23894392e+00  2.56267407e+00 -1.15743507e-02 -2.42436267e+00
  2.03824793e+00 -3.92504841e+00 -2.26973861e+00  1.24921866e+00
  1.74016734e+00 -1.09005667e-01 -6.27702130e-01  2.59591421e+00
 -4.22668929e+00  3.97227526e+00  7.77972395e-01  3.56333540e+00
 -1.93113008e+00  1.11554341e+00  4.25853910e-01 -1.44624218e+00
 -2.08847984e-01  5.88163216e-01  3.26025701e+00  1.80820449e+00
  1.77328919e+00  1.15071854e+00 -2.04241694e-01  1.18195005e+00
  3.09609901e+00  7.45412145e-01  4.04947783e+00  3.08144778e-01
  4.61939795e+00  3.53193718e+00  1.51960593e+00  5.52639112e+00
  1.12878294e+00 -8.18209789e-01  3.23849330e-01 -1.96325469e+00
  2.71782541e+00 -9.40249308e-01  5.12574419e-01 -1.81041721e-01
 -8.31922394e-01  4.18299554e+00  3.57787362e+00  1.29324695e+00
  4.42132432e+00  9.35334733e-01  1.07008218e+00  3.60953946e+00
  3.50494964e+00  1.90021235e+00  6.28497155e-01  3.25915911e-01
  4.07142062e+00 -1.82099710e+00  1.28718896e+00 -3.01120768e+00
 -2.22706567e+00  5.09828600e+00  4.12091035e-01  5.31622433e-01
  5.58166105e-01 -7.11325921e-02 -1.25281050e+00 -3.88229079e-01
  1.76480444e+00 -6.93686353e-01 -3.58080279e-01 -7.68521713e-01
  7.18696931e-01  2.92396669e+00  6.65243882e-01  2.15416328e+00
 -1.49351521e+00 -2.71222292e+00  5.26473707e+00  9.47312906e-01
 -4.81429007e-01 -2.62222727e+00 -1.04543527e+00  7.59241590e-01
  1.37320560e+00 -4.42079322e-01  1.15947838e+00  4.28891988e+00
 -1.73699618e+00  1.24819813e+00  1.73025843e+00 -1.61972311e+00
 -8.51815954e-01  2.99645739e+00 -1.70227445e-01  2.59035284e+00
 -1.25210124e+00  7.72498005e-01  2.31909855e+00 -1.30951678e+00
  2.86353058e+00 -7.98724277e-01 -1.14534173e+00  4.72907260e+00
  5.30810469e+00  2.55803374e-01  3.31677426e+00 -2.33219140e+00
  1.99184969e+00  1.40112574e+00  2.47451287e+00  1.26557444e+00
  2.57711421e+00 -5.94454824e-01  2.33765257e+00  4.15226339e+00
  2.35092462e+00  9.81968858e-01  2.51598445e+00 -1.22812581e+00
 -3.42829517e-01  4.64795092e+00  2.11691299e+00 -6.03232292e-03
 -1.20832048e+00  2.55923062e+00  4.68567211e+00  1.32169237e+00
  1.65364706e+00  1.78134081e+00 -4.32165120e-01  3.35589832e+00
 -9.62589022e-01 -2.61963990e+00 -3.79361667e+00  2.16888935e+00
  5.93512248e-02  2.01607382e+00  3.05636814e+00  5.70504112e+00
 -2.56733882e+00  5.92538600e-02 -6.25880056e-02  1.84142015e-02
  8.63406522e-01  7.55358808e-01  5.47577917e-01  2.80618573e+00
  2.55087412e+00  2.30273701e+00  4.78627067e-01 -2.44308822e+00
  1.17386767e+00  5.03439633e+00 -8.97117941e-01  2.76206360e+00
  1.32024327e+00  8.57480679e-01  1.36451186e+00  3.76942682e-01
  3.85489358e-01  7.15968417e-01  2.05937957e-01  1.30986277e+00
  2.03239250e+00  2.05301628e+00 -3.61318806e-01  1.21165220e+00
 -3.65511714e-02  2.29255163e+00 -4.40475421e-01 -2.16661886e-01
  7.52200066e-02 -1.64359691e+00  1.95815768e+00  8.82806184e-01
 -9.96088583e-01 -1.13234433e+00  2.31555982e+00  2.21504205e+00
  3.16990695e+00  5.67175876e-01  5.37613769e-01  1.45492853e+00
 -1.67778352e+00 -2.06962947e-01  7.59356230e-01  1.90154152e-01
  9.26646527e-01  7.47380632e-02  2.48854260e+00  7.36854562e-01
  2.66915982e+00  1.82598637e+00  5.89595316e-01  2.66803963e+00
  3.56026059e-01 -1.28428540e+00  1.85074527e+00 -2.44953635e+00
 -2.48191006e+00  1.54389457e+00  2.38479448e+00  3.27373175e+00
 -7.89098210e-01 -4.96566677e-01  4.04184463e-01 -3.34365065e+00
 -4.00443309e-01  8.89116431e-01  3.62800132e+00  4.81875841e+00
  1.16841349e-01 -4.99343752e-01  2.11231133e+00  3.00132193e+00
  1.28059669e+00  3.88012399e+00  3.18856383e-01  3.89978080e+00
 -2.24832780e-01 -1.88635674e+00 -5.39165877e-01  3.53742027e+00
  3.64591350e+00 -6.16283467e-01  5.92998524e+00  9.26339061e-01
  3.71640817e+00  1.64546020e+00  9.24779202e-01  4.48226545e+00
 -6.84518109e-01  5.46740401e+00  2.32971340e+00  1.28028388e+00
  1.54587425e+00 -1.45617539e+00  8.40024202e-01  3.58296709e+00
 -1.09276866e+00  5.22248318e-01  2.53336708e+00  3.91677508e+00
  4.70451647e+00  2.43472205e+00  2.22271896e+00  5.45651824e+00
  1.72984164e+00  1.04601218e+00  3.90610156e-01 -2.09359589e+00
 -2.87525849e-01  2.04532634e+00  2.20827491e+00  2.32725600e-01
  2.41521762e+00  4.38714853e+00  3.06699570e+00  3.05269743e+00
  1.93787334e-01  7.29186975e-01  7.98813143e-01  1.06349458e+00
  1.54857128e+00  4.77285370e-02  1.36544913e+00 -4.31461542e-01
  1.58687621e+00  6.90233423e-02  5.15686935e+00  1.14728956e+00
  1.31283319e-01  9.70377254e-01  2.26816649e+00  1.81646468e-02
  2.11993763e+00  1.67083529e+00 -4.13298277e-01  2.17875277e+00
 -3.38614215e-01  3.97268140e+00  3.59941454e+00  1.41228944e+00
  2.96021921e+00  4.06627369e+00  2.94459669e+00  3.91086715e+00
  4.38952894e+00  3.86996635e+00  1.46475647e+00  5.39218621e-02
 -6.97543657e-02  2.12145156e+00  1.56650762e+00  7.01894475e+00
  8.76376392e-01 -1.03585388e-01  5.56451177e-01  1.68359301e+00
  2.10910613e+00  8.50006337e-01 -3.50127494e+00  3.41125724e+00
 -7.52447751e-03 -6.51735845e-01 -2.29450614e-01  7.30799041e-01
  1.41258912e+00 -3.60992293e+00  4.00573572e-01  6.15736237e+00
 -1.06276325e+00  1.97710763e+00  9.37615256e-01  1.61605214e+00
  1.66465510e+00 -2.16201703e+00 -1.25264200e+00 -1.32597047e+00
  1.15325938e+00  1.58431547e+00  9.78992420e-01  4.21513638e+00
  1.40179001e+00  6.31445183e-01 -3.59821409e-01  1.83679080e+00
  4.78923098e+00 -6.20830883e-01  1.44618545e+00  2.40328480e+00
  5.01628213e-01  7.37441226e-01  1.74153623e+00  5.63818778e-01
  1.43096111e+00  3.09261881e+00  2.18485657e+00  2.59946202e-01
  6.48975245e-01 -2.17855062e+00  1.54793218e+00  4.15321272e+00
  2.64754194e+00 -1.51777026e+00  3.01488654e-01  2.15871250e+00
  1.96384715e+00 -1.50725913e-01 -9.33104995e-01 -2.82023881e+00
 -1.28909145e+00  5.62294505e-01  2.87714350e-01  1.50779828e+00
  1.07924535e+00  1.59373874e+00  2.21867700e+00 -2.21978951e+00
 -1.87299432e+00 -4.49973464e-01  2.43292671e+00  3.15064905e-01
  3.40247849e+00  7.70288612e-01 -9.62470803e-01  4.28083697e+00
  3.10862852e+00  4.61837942e-01  1.14415024e+00  2.96658169e+00
  1.38028044e+00  7.14972290e+00 -2.40664063e+00  3.19615995e+00
 -1.46387966e+00  4.16244300e+00 -1.56570831e+00  2.54225617e+00
  1.08847773e+00  2.24078167e+00  2.97676403e+00  4.01366833e+00
 -8.26938282e-01  2.91339165e+00  3.97827968e-01  8.96686821e-01
  1.46155102e+00  1.63066451e+00  1.24130143e+00  2.80625476e+00
  1.24064067e+00 -3.89838741e-01  2.91311149e+00  3.44129380e+00
 -7.07473445e-01 -2.45218488e+00  2.11459745e-01  3.51378035e+00
 -8.27793667e-01  5.72212469e+00  6.58122801e-02  1.28846071e+00
 -6.60108097e-01  1.79497569e+00 -1.93276863e+00  1.53452436e+00
  1.86024850e-01  4.56280000e+00  1.02697364e-01 -3.26733299e+00
  1.68391865e+00  4.04694697e+00  2.60718890e+00 -1.36601031e+00
 -6.03412491e-01 -1.56911144e+00 -1.80172998e+00 -1.30305311e+00
  3.95662862e+00  1.43741940e+00 -7.85208223e-02  2.32463786e+00
  1.35137423e+00 -5.22346110e-01  1.53809904e+00  2.15641175e+00
  2.97245039e+00  8.49721456e-01  2.73741656e+00 -2.37095900e-01
  2.86693363e+00 -7.27985243e-01  2.84008215e+00 -4.81080447e+00
 -1.45846065e+00  1.16308986e+00  1.51385049e+00  2.77482369e+00
  4.37514421e+00  7.28389023e-01 -1.41843266e+00 -1.96880542e+00
  3.21999776e+00  1.17162458e+00 -1.57043695e+00  5.20870397e+00
  2.85827402e+00  4.10370520e+00  1.87099505e-02  2.43799907e+00
  2.62347210e+00 -1.87778073e+00  4.01028543e-01  2.04253807e+00
 -1.47425376e+00  4.42807395e+00 -3.88962416e-01  1.23563363e+00
 -7.61261147e-02  2.86536027e+00  3.12453122e+00 -1.92503349e-01
 -1.32446962e-01 -2.54538408e+00  7.72744780e-01 -3.27845715e+00
 -1.24223847e+00  1.12828593e+00  4.69298903e+00  2.53519847e+00
  2.07862846e+00  2.38340138e+00  1.07683439e+00 -3.49695210e-01
 -5.73551562e-01  4.21806609e+00  2.01086238e+00  1.68158263e+00
 -2.38389984e+00  2.55380746e+00 -2.15321353e-01  3.52779835e+00
  1.14351974e+00  4.57733904e+00  6.70772911e-01 -7.13142044e-01
  2.07820415e+00  4.55755256e+00  1.70295138e+00 -4.60897405e+00
  2.62963640e+00 -2.36384318e-01 -1.08321707e+00 -4.94012305e-01
  2.52232037e+00 -6.82569797e-02 -1.92763969e+00  2.00176787e+00
  1.03906052e+00  1.42135697e+00 -1.33099974e+00  1.71520779e+00
  1.83802888e+00  1.26353456e+00  5.19358733e-01 -2.71991759e+00
 -7.48832656e-02 -2.37373278e+00  3.95027776e+00 -2.65930699e-01
 -1.02080011e+00  4.13978936e+00  1.47303433e+00  1.20200713e+00
  2.86511073e+00 -1.14555807e+00 -1.63527529e+00  4.11195430e+00
 -6.21731535e-01  1.79006615e+00 -2.17127619e+00  4.61236732e+00
  2.81309598e+00 -1.36348590e+00  8.92353071e-01 -5.75463145e-02
  2.71296058e+00 -5.68055864e-01  8.28318207e-01  5.33696652e-01
  4.81460202e+00  1.02912783e+00  6.48335903e-01  1.88355821e+00
  1.13909545e+00 -1.49217829e+00  2.96333749e+00 -1.01882231e-01
  1.17781850e+00  1.09564320e+00 -2.04677373e+00  5.83601117e-01
  1.72178419e+00  3.77122123e+00  1.60335713e+00 -1.34929223e-01
  1.66608771e+00  3.09546803e+00  4.95595739e+00  5.60451841e-01
  4.63243934e+00  1.20105853e+00 -1.78174319e+00  3.38122714e+00
  9.42946379e-01  1.04106779e+00  1.38865450e+00  1.73360932e+00
  9.88494684e-01  2.76643560e+00  1.46630011e+00  9.49019709e-02
  1.93675755e+00  5.58273196e-01  2.65831056e+00 -1.15086449e+00
  4.73103582e-01  1.68014507e-01  2.32104357e+00  8.07146328e-01
  1.64629761e+00  2.88582013e+00 -1.62762025e+00  2.95669648e+00
 -1.08629516e+00  2.68077784e+00  1.01351994e+00  9.96035598e-01
  1.05960782e+00 -1.26912783e+00  8.28920405e-01  3.01755355e+00
  1.58948582e+00 -2.03019801e+00 -2.28552327e+00  3.33785502e+00
  4.94288554e-01  2.14424127e-01 -7.98600376e-01 -3.22468531e-01
  2.44993399e+00  2.98100762e+00  9.69545715e-01  4.11243709e+00
  1.81889262e-01  4.56586924e+00  3.78532945e+00  1.43999979e-01
  9.37793233e-01 -9.17202476e-01  5.97038083e+00  4.92006436e-01
  1.97978057e+00 -1.64312058e+00  1.81890281e+00 -2.61289256e-01
 -1.67427508e+00 -1.63314129e+00  3.63923707e+00 -1.01275452e+00
  9.58993241e-01  3.63122080e+00  2.31316899e+00 -1.54267143e+00
  1.76717030e+00  1.38232353e+00  2.34393691e+00  1.83258648e+00
  1.70355559e+00 -4.99240868e-01  1.62316010e+00 -5.07321587e-01
  2.67011051e+00  2.86041728e+00 -1.41138801e-01  3.59701926e+00
  4.41619176e+00  3.90586665e+00 -1.70452335e+00  4.44640690e-01
 -9.75135388e-01  3.40534214e+00  3.41456357e+00  1.18599730e+00
 -2.45107964e+00  3.09782085e+00 -9.09961243e-01 -5.20727780e-02
 -3.64257768e+00  4.45388330e+00 -1.70372870e+00  1.87005864e+00]

(0.9833073950025236, 1.9340481476735356)

pandas

• DataFrame functionality
  • everything is "methods" based, though
• "SQL"-like capabilities
• design focusses on timeseries (and correspondingly, indexes)

import pandas as pd

dataset = 'https://raw.githubusercontent.com/mwaskom/seaborn-data/master/penguins.csv'
penguins = pd.read_csv(dataset, dtype={key:'category' for key in ['species','island','sex']})
penguins.head()

	species	island	bill_length_mm	bill_depth_mm	flipper_length_mm	body_mass_g	sex
0	Adelie	Torgersen	39.1	18.7	181.0	3750.0	MALE
1	Adelie	Torgersen	39.5	17.4	186.0	3800.0	FEMALE
2	Adelie	Torgersen	40.3	18.0	195.0	3250.0	FEMALE
3	Adelie	Torgersen	NaN	NaN	NaN	NaN	NaN
4	Adelie	Torgersen	36.7	19.3	193.0	3450.0	FEMALE

penguins.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 344 entries, 0 to 343
Data columns (total 7 columns):
 #   Column             Non-Null Count  Dtype   
---  ------             --------------  -----   
 0   species            344 non-null    category
 1   island             344 non-null    category
 2   bill_length_mm     342 non-null    float64 
 3   bill_depth_mm      342 non-null    float64 
 4   flipper_length_mm  342 non-null    float64 
 5   body_mass_g        342 non-null    float64 
 6   sex                333 non-null    category
dtypes: category(3), float64(4)
memory usage: 12.1 KB

# like the R `summrary()` function
penguins.describe()

	bill_length_mm	bill_depth_mm	flipper_length_mm	body_mass_g
count	342.000000	342.000000	342.000000	342.000000
mean	43.921930	17.151170	200.915205	4201.754386
std	5.459584	1.974793	14.061714	801.954536
min	32.100000	13.100000	172.000000	2700.000000
25%	39.225000	15.600000	190.000000	3550.000000
50%	44.450000	17.300000	197.000000	4050.000000
75%	48.500000	18.700000	213.000000	4750.000000
max	59.600000	21.500000	231.000000	6300.000000

import matplotlib.pyplot as plt
tabs = []
fig = plt.figure(figsize=[8,4])
ax = fig.subplots(2,2).flatten()
i = 0
for col in penguins:
    if penguins.dtypes[col]=='float64':
        penguins[[col]].plot(kind='kde', ax=ax[i])
        i+=1
    elif penguins.dtypes[col]=='category':
        tabs += [pd.DataFrame(penguins[col].value_counts(), columns=[col])]
    else:
        pass

plt.tight_layout()
plt.show()
_=[display(tab) for tab in tabs]

	species
Adelie	152
Gentoo	124
Chinstrap	68

	island
Biscoe	168
Dream	124
Torgersen	52

	sex
MALE	168
FEMALE	165

strikes_path = 'http://lib.stat.cmu.edu/datasets/strikes'
strikes = pd.read_csv(strikes_path, skiprows=18, header=None,
                      delim_whitespace=True)
strikes.columns = ['Country', 'Year', 'Stike_Volume', 'Unemplyment',
                    'Inflation', 'Socialist_Party_Representation',
                    'Unionization']
strikes[['Year']] = strikes[['Year']].astype(type(0))

strikes.head()

	Country	Year	Stike_Volume	Unemplyment	Inflation	Socialist_Party_Representation	Unionization
0	1.0	1951	296.0	1.3	19.8	43.0	0.375
1	1.0	1952	397.0	2.2	17.2	43.0	0.375
2	1.0	1953	360.0	2.5	4.3	43.0	0.375
3	1.0	1954	300.0	1.7	0.7	47.0	0.375
4	1.0	1955	326.0	1.4	2.0	38.5	0.375

SnP_path = 'http://lib.stat.cmu.edu/datasets/spdc2693'
SnP = pd.read_csv(SnP_path, skiprows=5, header=None,
                  delim_whitespace=True)
SnP.columns = ['Date', 'Close']
SnP['Date'] = SnP.Date.apply(lambda x: pd.to_datetime('19'+str(x), format='%Y%m%d'))
SnP['Year'] = SnP.Date.apply(lambda x: x.year)

SnP.head()

	Date	Close	Year
0	1926-01-08	12.78	1926
1	1926-01-15	12.52	1926
2	1926-01-22	12.45	1926
3	1926-01-29	12.74	1926
4	1926-02-05	12.87	1926

SnP_strikes = SnP.merge(strikes, on='Year', how='inner')
SnP_strikes.set_index('Date', inplace=True)
country_codes = {1.0: 'AusT',
                 2.0: 'AusA',
                 3.0: 'Bel',
                 4.0: 'Can',
                 5.0: 'Den',
                 6.0: 'Fin',
                 7.0: 'Fra',
                 8.0: 'Ger',
                 9.0: 'Ire',
                 10.0: 'Ita',
                 11.0: 'Jap',
                 12.0: 'Ned',
                 13.0: 'Nwz',
                 14.0: 'Nor',
                 15.0: 'Swe',
                 16.0: 'Swi',
                 17.0: 'UK',
                 18.0: 'Usa'}
SnP_strikes['Country'] = SnP_strikes.Country.map(country_codes)
strikes[['Country']] = pd.Categorical(strikes['Country'])

fig, ax = plt.subplots(2,1, figsize=(15,13))
#apply(lambda x: np.log(x) if x.name=='Stike_Volume' else x).\
SnP_strikes.groupby('Country').rolling(200).mean().reset_index(0).groupby('Country')['Unemplyment'].plot(ax=ax[0])
ax[0].set_title('Unemployment (%)')
ax[0].legend(loc='upper center')

SnP_strikes['Close'].plot(ax=ax[1])
ax[1].set_title('S&P 500 Closing Values')

Text(0.5, 1.0, 'S&P 500 Closing Values')

seaborn

• matplotlib 2.0

SnP_strikes[SnP_strikes.Country.apply(lambda x: x in ['Usa','UK'])].\
    groupby(by=['Year','Country']).max()

		Close	Stike_Volume	Unemplyment	Inflation	Socialist_Party_Representation	Unionization
Year	Country
1951	UK	23.85	81.0	0.9	9.7	47.2	0.375
	Usa	23.85	466.0	3.2	8.0	51.0	0.000
1952	UK	26.59	86.0	1.4	6.1	47.2	0.375
	Usa	26.59	1190.0	2.9	2.2	51.0	0.000
1953	UK	26.66	104.0	1.3	1.9	47.2	0.375
...	...	...	...	...	...	...	...
1983	Usa	172.65	192.0	9.5	3.2	46.0	0.000
1984	UK	170.41	1278.0	11.2	5.0	32.2	0.375
	Usa	170.41	89.0	7.4	4.3	46.0	0.000
1985	UK	212.02	298.0	11.5	6.1	32.2	0.375
	Usa	212.02	73.0	7.1	3.6	47.0	0.000

70 rows × 6 columns

import seaborn as sns
SnP_strikes_US_UK = SnP_strikes[SnP_strikes.Country.apply(lambda x: x in ['Usa','UK'])].\
    groupby(by=['Year','Country']).max().reset_index(1).dropna()
#SnP_strikes_US_UK.Country.cat.remove_unused_categories(inplace=True)

p = sns.pairplot(SnP_strikes_US_UK.iloc[:,:-1], hue="Country")
p.map_lower(sns.kdeplot, levels=4, color=".2")
p.map_upper(sns.histplot)

<seaborn.axisgrid.PairGrid at 0x7fbdb93f99a0>

Scikit-Learn

• do Machine Learning with sklearn
• do stats with pandas+statsmodels (not shown)

#https://scikit-learn.org/stable/auto_examples/gaussian_process/plot_gpc_iris.html#sphx-glr-auto-examples-gaussian-process-plot-gpc-iris-py
    
from sklearn import datasets    
from sklearn.gaussian_process import GaussianProcessClassifier
from sklearn.gaussian_process.kernels import RBF

# import some data to play with
iris = datasets.load_iris()
X = iris.data[:, :2]  # we only take the first two features.
y = np.array(iris.target, dtype=int)

h = .02  # step size in the mesh

kernel = 1.0 * RBF([1.0])
gpc_rbf_isotropic = GaussianProcessClassifier(kernel=kernel).fit(X, y)
kernel = 1.0 * RBF([1.0, 1.0])
gpc_rbf_anisotropic = GaussianProcessClassifier(kernel=kernel).fit(X, y)

# create a mesh to plot in
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
                     np.arange(y_min, y_max, h))

titles = ["Isotropic RBF", "Anisotropic RBF"]
plt.figure(figsize=(10, 5))
for i, clf in enumerate((gpc_rbf_isotropic, gpc_rbf_anisotropic)):
    # Plot the predicted probabilities. For that, we will assign a color to
    # each point in the mesh [x_min, m_max]x[y_min, y_max].
    plt.subplot(1, 2, i + 1)

    Z = clf.predict_proba(np.c_[xx.ravel(), yy.ravel()])

    # Put the result into a color plot
    Z = Z.reshape((xx.shape[0], xx.shape[1], 3))
    plt.imshow(Z, extent=(x_min, x_max, y_min, y_max), origin="lower")

    # Plot also the training points
    plt.scatter(X[:, 0], X[:, 1], c=np.array(["r", "g", "b"])[y],
                edgecolors=(0, 0, 0))
    plt.xlabel('Sepal length')
    plt.ylabel('Sepal width')
    plt.xlim(xx.min(), xx.max())
    plt.ylim(yy.min(), yy.max())
    plt.xticks(())
    plt.yticks(())
    plt.title("%s, LML: %.3f" %
              (titles[i], clf.log_marginal_likelihood(clf.kernel_.theta)))

plt.tight_layout()

#https://scikit-learn.org/stable/auto_examples/ensemble/plot_gradient_boosting_regularization.html#sphx-glr-auto-examples-ensemble-plot-gradient-boosting-regularization-py
    
from sklearn import ensemble

X, y = datasets.make_hastie_10_2(n_samples=12000, random_state=1)
X = X.astype(np.float32)

# map labels from {-1, 1} to {0, 1}
labels, y = np.unique(y, return_inverse=True)

X_train, X_test = X[:2000], X[2000:]
y_train, y_test = y[:2000], y[2000:]

original_params = {'n_estimators': 1000, 'max_leaf_nodes': 4, 'max_depth': None, 'random_state': 2,
                   'min_samples_split': 5}

plt.figure()

for label, color, setting in [('No shrinkage', 'orange',
                               {'learning_rate': 1.0, 'subsample': 1.0}),
                              ('learning_rate=0.1', 'turquoise',
                               {'learning_rate': 0.1, 'subsample': 1.0}),
                              ('subsample=0.5', 'blue',
                               {'learning_rate': 1.0, 'subsample': 0.5}),
                              ('learning_rate=0.1, subsample=0.5', 'gray',
                               {'learning_rate': 0.1, 'subsample': 0.5}),
                              ('learning_rate=0.1, max_features=2', 'magenta',
                               {'learning_rate': 0.1, 'max_features': 2})]:
    params = dict(original_params)
    params.update(setting)

    clf = ensemble.GradientBoostingClassifier(**params)
    clf.fit(X_train, y_train)

    # compute test set deviance
    test_deviance = np.zeros((params['n_estimators'],), dtype=np.float64)

    for i, y_pred in enumerate(clf.staged_decision_function(X_test)):
        # clf.loss_ assumes that y_test[i] in {0, 1}
        test_deviance[i] = clf.loss_(y_test, y_pred)

    plt.plot((np.arange(test_deviance.shape[0]) + 1)[::5], test_deviance[::5],
            '-', color=color, label=label)

plt.legend(loc='upper left')
plt.xlabel('Boosting Iterations')
plt.ylabel('Test Set Deviance')

Text(0, 0.5, 'Test Set Deviance')

plotly

• primary language is python

# https://plotly.com/python/visualizing-mri-volume-slices/
# https://www.geeksforgeeks.org/animated-data-visualization-using-plotly-express/

import time
import numpy as np

from skimage import io

vol = io.imread("https://s3.amazonaws.com/assets.datacamp.com/blog_assets/attention-mri.tif")
volume = vol.T
r, c = volume[0].shape

# Define frames
import plotly.graph_objects as go
nb_frames = 68

fig = go.Figure(frames=[go.Frame(data=go.Surface(
    z=(6.7 - k * 0.1) * np.ones((r, c)),
    surfacecolor=np.flipud(volume[67 - k]),
    cmin=0, cmax=200
    ),
    name=str(k) # you need to name the frame for the animation to behave properly
    )
    for k in range(nb_frames)])

# Add data to be displayed before animation starts
fig.add_trace(go.Surface(
    z=6.7 * np.ones((r, c)),
    surfacecolor=np.flipud(volume[67]),
    colorscale='Gray',
    cmin=0, cmax=200,
    colorbar=dict(thickness=20, ticklen=4)
    ))


def frame_args(duration):
    return {
            "frame": {"duration": duration},
            "mode": "immediate",
            "fromcurrent": True,
            "transition": {"duration": duration, "easing": "linear"},
        }

sliders = [
            {
                "pad": {"b": 10, "t": 60},
                "len": 0.9,
                "x": 0.1,
                "y": 0,
                "steps": [
                    {
                        "args": [[f.name], frame_args(0)],
                        "label": str(k),
                        "method": "animate",
                    }
                    for k, f in enumerate(fig.frames)
                ],
            }
        ]

# Layout
fig.update_layout(
         title='Slices in volumetric data',
         width=600,
         height=600,
         scene=dict(
                    zaxis=dict(range=[-0.1, 6.8], autorange=False),
                    aspectratio=dict(x=1, y=1, z=1),
                    ),
         updatemenus = [
            {
                "buttons": [
                    {
                        "args": [None, frame_args(50)],
                        "label": "▶", # play symbol
                        "method": "animate",
                    },
                    {
                        "args": [[None], frame_args(0)],
                        "label": "◼", # pause symbol
                        "method": "animate",
                    },
                ],
                "direction": "left",
                "pad": {"r": 10, "t": 70},
                "type": "buttons",
                "x": 0.1,
                "y": 0,
            }
         ],
         sliders=sliders
)

fig.show()

! yes y | conda install -c conda-forge ffmpeg

# https://matplotlib.org/3.1.0/gallery/animation/unchained.html

import numpy as np
import matplotlib.pyplot as plt
from IPython.display import HTML
from matplotlib import animation, rc
rc('animation', html='html5')
%matplotlib notebook

# Fixing random state for reproducibility
np.random.seed(19680801)


# Create new Figure with black background
fig = plt.figure(figsize=(8, 8), facecolor='black')

# Add a subplot with no frame
ax = plt.subplot(111, frameon=False)

# Generate random data
data = np.random.uniform(0, 1, (64, 75))
X = np.linspace(-1, 1, data.shape[-1])
G = 1.5 * np.exp(-4 * X ** 2)

# Generate line plots
lines = []
for i in range(len(data)):
    # Small reduction of the X extents to get a cheap perspective effect
    xscale = 1 - i / 200.
    # Same for linewidth (thicker strokes on bottom)
    lw = 1.5 - i / 100.0
    line, = ax.plot(xscale * X, i + G * data[i], color="w", lw=lw)
    lines.append(line)

# Set y limit (or first line is cropped because of thickness)
ax.set_ylim(-1, 70)

# No ticks
ax.set_xticks([])
ax.set_yticks([])

# 2 part titles to get different font weights
ax.text(0.5, 1.0, "MATPLOTLIB ", transform=ax.transAxes,
        ha="right", va="bottom", color="w",
        family="sans-serif", fontweight="light", fontsize=16)
ax.text(0.5, 1.0, "UNCHAINED", transform=ax.transAxes,
        ha="left", va="bottom", color="w",
        family="sans-serif", fontweight="bold", fontsize=16)


def update(*args):
    # Shift all data to the right
    data[:, 1:] = data[:, :-1]

    # Fill-in new values
    data[:, 0] = np.random.uniform(0, 1, len(data))

    # Update data
    for i in range(len(data)):
        lines[i].set_ydata(i + G * data[i])

    # Return modified artists
    return lines

# Construct the animation, using the update function as the animation director.
anim = animation.FuncAnimation(fig, update, interval=50)
#HTML(anim.to_html5_video())
anim